Ignorance is Almost Bliss: Near-Optimal Stochastic Matching With Few Queries

The stochastic matching problem deals with finding a maximum matching in a graph whose edges are unknown but can be accessed via queries. This is a special case of stochastic $k$-set packing, where the problem is to find a maximum packing of sets, each of which exists with some probability. In this paper, we provide edge and set query algorithms for these two problems, respectively, that provably achieve some fraction of the omniscient optimal solution. Our main theoretical result for the stochastic matching (i.e., $2$-set packing) problem is the design of an \emph{adaptive} algorithm that queries only a constant number of edges per vertex and achieves a $(1-\epsilon)$ fraction of the omniscient optimal solution, for an arbitrarily small $\epsilon>0$. Moreover, this adaptive algorithm performs the queries in only a constant number of rounds. We complement this result with a \emph{non-adaptive} (i.e., one round of queries) algorithm that achieves a $(0.5 - \epsilon)$ fraction of the omniscient optimum. We also extend both our results to stochastic $k$-set packing by designing an adaptive algorithm that achieves a $(\frac{2}{k} - \epsilon)$ fraction of the omniscient optimal solution, again with only $O(1)$ queries per element. This guarantee is close to the best known polynomial-time approximation ratio of $\frac{3}{k+1} -\epsilon$ for the \emph{deterministic} $k$-set packing problem [Furer and Yu, 2013] We empirically explore the application of (adaptations of) these algorithms to the kidney exchange problem, where patients with end-stage renal failure swap willing but incompatible donors. We show on both generated data and on real data from the first 169 match runs of the UNOS nationwide kidney exchange that even a very small number of non-adaptive edge queries per vertex results in large gains in expected successful matches

Spin-lattice coupling mediated giant magnetodielectricity across the spin reorientation in Ca2FeCoO5

The structural, phonon, magnetic, dielectric, and magneto dielectric responses of the pure bulk Brownmillerite compound Ca2FeCoO5 are reported. This compound showed giant magneto dielectric response (10%-24%) induced by strong spin-lattice coupling across its spin reorientation transition (150-250 K). The role of two Debye temperatures pertaining to differently coordinated sites in the dielectric relaxations is established. The positive giant magneto-dielectricity is shown to be a direct consequence of the modulations in the lattice degrees of freedom through applied external field across the spin reorientation transition. Our study illustrates novel control of magneto-dielectricity by tuning the spin reorientation transition in a material that possess strong spin lattice coupling.Comment: 7 pages, 12 figure

Modulated structure in the martensite phase of Ni1.8Pt0.2MnGa: a neutron diffraction study

7M orthorhombic modulated structure in the martensite phase of Ni1.8Pt0.2MnGa is reported by powder neutron diffraction study, which indicates that it is likely to exhibit magnetic field induced strain. The change in the unit cell volume is less than 0.5% between the austenite and martensite phases, as expected for a volume conserving martensite transformation. The magnetic structure analysis shows that the magnetic moment in the martensite phase is higher compared to Ni2MnGa, which is in good agreement with magnetization measurement

Formulation and evaluation of controlled release ethylcellulose and polyethylene glycol microspheres containing metoprolol tartrate.

Metoprolol tartrate is rapidly absorbed from both gastric and intestinal regions, after oral administration. To retard the release rate of the metoprolol tartrate, microspheres were prepared with varying concentrations of a mixture containing ethylcellulose and polyethylene glycol-6000. The prepared microspheres were evaluated for various physicochemical characteristics and in vitro drug release. The percent yield of microspheres was in the range of 75.2-87.3%. The particle size of microspheres was found to be in the range of 73.2-85.5 μm. Fourier transform-infrared spectral analysis and differential scanning calorimetry concluded the absence of any interaction between the drug and the carriers. The release time profile of metoprolol tartrate from microspheres in 0.1 N hydrochloric acid solution was to the extent of 33.4-60.2%. The complete release of metoprolol tartrate occurred from MPT-3 and MPT-4 in phosphate buffer solution (pH 7.4) within 8 and 7 h, respectively, whereas the incomplete release (72.3%) occurred from MPT-1. Nearly, the complete release (98.5%) of metoprolol occurred from MPT-2 in 10 h. Formulation MPT-2 would be a preferred formulation. The release of metoprolol involves diffusion rate limited (R2 = 0.9865) as a mechanism from drug release. The prepared microspheres of metoprolol tartrate eliminate the need for multiple dosing and provide patient compliance